Calculation Method Of Multi-loop Coupling Mechanisms Mobility Based On Geometric Algebra

Multi-loop coupling mechanisms have been used in aerospace,bionic robots,deep space exploration,architectural design and outdoor activities.The degree of freedom,as the basic problem of the mechanism,is of great significance in the development and application of multi-loop coupling mechanisms.The coupling characteristics of the limbs of the multi-loop coupling mechanisms have always been the key and difficult point in proposing a universal calculation method of multi-loop coupling mechanisms.This dissertation takes this as the starting point for research,the full text and the main work and achievements are as follows:A calculation method for the degree of freedom of multi-loop coupling mechanisms under the framework of geometric algebra is proposed.And the coupling components are equivalent to obtain the topology diagram of the mechanism,and the shortest limb connecting the frame and the output component is found.By modifying the twist space coupled with the coupling closed loop on the limb,the twist space of the limb is corrected.Finally,the intersection of all the modified limb twist spaces is obtained to obtain the twist space of the output link.By decoupling the twist space of the output link into the corresponding single-degree-of-freedom analytical formula,the properties of the output link’s full-cycle degree of freedom can be obtained.According to the distribution of coupled closed loops,multi-loop coupling mechanisms are classified: single-limb coupling,inter-limb coupling and hybrid coupling multi-loop coupling mechanisms.A calculation method for the degrees of freedom of single-limb and inter-limb coupled multi-loop coupling mechanisms under the framework of geometric algebra is proposed.The coupling closed-loop part on each limb is corrected sequentially in the order from the rack to the output component.Only the influence of the closed loop on the coupled part of one limb is considered in each correction.The corrected limb twist space is obtained by taking the union of all the modified parts and the uncoupled twist.The intersection of all limb twist spaces is obtained to obtain the twist space of the output link.A calculation method for the degree of freedom of multi-loop coupling mechanisms with single limb and inter-limb coupling under the framework of geometric algebra is proposed.For each limb and the coupling part of the closed loop,follow the sequence from the base to the output link and modify it sequentially.Only the effect of closed loop on one limb is considered in each correction.The union of all the modified parts and the uncoupled twists results in the modified limb twist space.The intersection of all the modified limb twist spaces is obtained to obtain the twist space of the output link.A calculation method for the degree of freedom of multi-loop coupling mechanisms under the framework of geometric algebra is proposed.When there is coupling in the closed loop,it is necessary to follow the principle of analyzing the smaller closed loop at first and modify the coupled part of the closed loop first to reduce unnecessary calculation costs.The union of all the modified parts and the uncoupled twists results in the modified limb twist space.The intersection of all limb twist spaces is obtained to obtain the twist space of the output link.A method for selecting an optimal drive scheme for multi-loop coupling mechanisms based on input transmission index(ITI)is proposed.According to the independent variables in the analytical formula of the output degree of freedom,a feasible driving scheme is selected,and by calculating the ITI distribution of each group of driving schemes within the working range,a group with better performance distribution is selected as the output scheme of the mechanism,which is the output scheme of the multiloop coupling mechanisms A new way of thinking is put forward for the selection of driving scheme.After the above work,the universal feasibility of the calculation method for the degree of freedom of multi-loop coupling mechanisms based on geometric algebra proposed in this dissertation is proved to a certain extent,and a new solution to the problem of drive selection of multi-loop coupling mechanisms is proposed.